⇦Chinese Physics Letters, 2019, Vol. 36, No. 1, Article code 010501 A New Probe: AFM Measurements for Random Disorder Systems * R. Salci1, D. A. Acar1, O. Oztirpan1, M. Ramazanoglu1,2** Affiliations 1Physics Engineering Department, Istanbul Technical University, Maslak 34469, Istanbul, Turkey 2Brockhouse Institute for Materials Research, Hamilton, ON L8S 4M1 Canada Received 3 September 2018, online 25 December 2018 *Supported by TUBITAK under Grant No 115F315.
**Corresponding author. Email: ramazanoglum@itu.edu.tr Citation Text: Salci R, Acar D A, Oztirpan O and Ramazanoglu M 2019 Chin. Phys. Lett. 36 010501    Abstract We study the quenched random disorder (QRD) effects created by aerosil dispersion in the octylcyanobiphenyl (8CB) liquid crystal (LC) using atomic force microscopy technique. Gelation process in the 8CB+aerosil gels yields a QRD network which also changes the surface topography. By increasing the aerosil concentration, the original smooth pattern of LC sample surfaces is suppressed by the emergence of a fractal aerosil surface effect and these surfaces become more porous, rougher and they have more and larger crevices. The dispersed aerosil also serves as pinning centers for the liquid crystal molecules. It is observed that via the diffusion-limited-aggregation process, aerosil nano-particles yield a fractal-like surface pattern for the less disordered samples. As the aerosil dispersion increases, the surface can be described by more aggregated regions, which also introduces more roughness. Using this fact, we show that there is a net correlation between the short-range ordered x-ray peak widths (the results of previous x-ray diffraction experiments) and the calculated surface roughness. In other words, we show that these QRD gels can also be characterized by their surface roughness values. DOI:10.1088/0256-307X/36/1/010501 PACS:05.40.-a, 61.30.Vx, 61.30.Hn, 61.43.-j, 68.37.Ps © 2019 Chinese Physics Society Article Text Because liquid crystals (LCs) show rich phase transition capabilities within several mesogenic phases, they have been a popular subject for sciences where disorder effects are studied within controlled random forces. For almost two decades, aerogel and aerosil nano-particles were used to create the random disorders in LC phases.[1-3] In these previous works, the aim was to study the randomness imposed on the LC order parameters where the amount of dispersed silica nano-particles simply served as the control mechanism of the created QRD. The first experiments were conducted on LC+aerogel samples using mainly heat capacity and x-ray scattering techniques.[1,2] It was observed from these measurements that the aerogel dispersion couples with the nematic director and smectic order, which creates a random gel network. Later, the quenched disorder effects of aerosil were found to be more interesting than those created by aerogels and many subsequent LC+aerosil experiments followed.[3-6] The LC+aerosil systems are particularly important because very low random disorder effects can be created within these gels. This is achieved with the hydroxyl groups surrounding the silica nano-particles. Each hydroxyl covered silica sphere surface affects another, creating fractal links of solid nano-particles in the LC host environment.[3,4] These links yield a weak network giving flexibility to the LC+aerosil gels. In this Letter, we investigate the surface characteristics of LC+aerosil samples using atomic force microscopy (AFM) techniques. Studying the surface topography has the advantage of correlating the results to the well-known characteristics of these gels. Randomly pinned LC orders have so far been investigated by several characteristic parameters, including random disorder correlation length $\xi_{\rm RD}$, enthalpy $\delta H$, and heat capacity $\Delta C_{\rm p}$. These parameters are measured by x-ray diffraction and calorimetry spectroscopy techniques, respectively. As an alternative to these techniques, we use the surface roughness to characterize the same effect for the first time. To reach these goals, 4-cyano-4-octylbiphenyl (8CB) LC was selected. In this work, we study a second-order phase transition in which short ranged correlations in smectic $A$ phase created by the influence of aerosil dispersion. All of the measurements that are shown and discussed here focus on the topographical changes on the sample surfaces. In that sense, this can be categorized as a surface science study of LC+aerosil gels. However, the central idea is the study of the correlation between the known short-ranged smectic order characteristics and the surface topography of the gel samples. The 8CB LC was purchased from Frinton Lab[7] and we performed our sample preparation steps without any purification process. Hydrophilic aerosil was obtained from Evonik Corp.[8] Here, only type 300, which is $\sim$7 nm in diameter, silica nano-particles were used. The Brunauer–Emmet–Teller (BET) surface area for these nano-particles is listed as 300 m$^2$g$^{-1}$.[8] Because they are very susceptible to water contamination, a drying process at $T\simeq500$ K under 10$^{-2}$ atm vacuum was used for several days prior to mixing with LCs. In this study, the samples were distinguished with a parameter known as aerosil mass density $\rho_{\rm s}$ which can be derived from $$ \frac{1}{\rho_{\rm s}}=\frac{1}{\rho}-\frac{1}{\rho_{\rm aerosil}},~~ \tag {1} $$ where $$ \rho=\frac{m_{\rm aerosil}}{V_{\rm tot}},~~ \tag {2} $$ and $\rho_{\rm aerosil}=2.2$ g/cm$^3$,[8] with $V_{\rm tot}=V_{\rm LC}+V_{\rm aerosil}$. Thus Eq. (1) can also be simplified to $$ \rho_{\rm s}=\frac{m_{\rm aerosil}}{V_{\rm LC}},~~ \tag {3} $$ which is more useful for categorizing the sample disorder strength that is simply the ratio between mass of the aerosil and the volume of the LC. Stoichiometric amounts of 8CB and the aerosil were mixed in high purity ethanol and sonicated at $\sim$300 K for around half an hour. High quality 8CB+aerosil mixtures were successfully obtained.[9-12] The mixtures were then placed on a hot plate that was held at 310$\pm$0.5 K constant temperature. The rest of the drying, or in other words gelation, process was performed at a temperature $\sim$307 K close to the isotropic phase of the LC. For AFM measurements, samples were transferred on microscope glass specimen holders. Drying of the high aerosil concentration samples produced small cracks, where it was possible to hold them. These samples were placed on glass holders using tweezers. However, low aerosil concentration samples; $\rho_{\rm s}\lesssim0.347$ g/cm$^3$ were collected with a spatula and an adequate amount of sample was placed on the glass or a Si wafer surface. The gelation procedure creates mainly two groups of LC+aerosil gels depending on the aerosil amount.[3] The samples with $\rho_{\rm s}\sim0.2$ g/cm$^3$ and higher densities are found to be more rigid and their physical attributes resemble the LC+aerogel samples.[2] During the process of sample transfer, samples were carefully held at the same drying temperature lest the LC+aerosil network be mechanically perturbed and put into temperature stress. We also avoided any accidental crystallization and phase separation issues in the samples. In that sense, 8CB LC is one of the best and easiest LC samples to work with because it crystallizes at $T_{\rm C}\sim290$ K ($\sim$17$^{\circ}\!$C), which is lower than common room temperatures. It has nematic to smectic $A$ and isotropic to nematic phase transitions at $T_{\rm NA}\sim 306.97$ K and $T_{\rm NI}\sim 313.98$ K, respectively.[5,6] The AFM scans were conducted at the ITUNANO Laboratory clean room facility where the temperature and humidity were held at 296.15 K and $\sim$35% constantly.[13] This temperature is just 6 K over the crystallization temperature of the 8CB so that the AFM scans were conducted on the well-formed and short-range ordered smectic $A$ phases of the 8CB+aerosil gels surfaces. The surface topography was investigated by a profilometer (a Ziess Axio CSM 700 type profilometer was used) for the two highest aerosil mass density samples. The AFM scans were analyzed by an NMI image analyzer ver 1.4 software.[13] The atomic force microscopy (AFM) data are shown in Fig. 1 for seven different pictures of seven different aerosil mass density ($\rho_{\rm s}$) values. Here, the data was only interpreted with the surface topography value; surface roughness $\langle R\rangle$ which can be given as[13] $$ \langle R\rangle=\frac{1}{MN} \sum_{h=0}^{M-1}\sum_{k=0}^{N-1}\mid z(h,k)\mid,~~ \tag {4} $$ where $z(h,k)$ denotes the normalized height distribution data with the mean surface height distribution being subtracted.[14] The soft and gel-like structure of low aerosil density samples allow only non-contact mode scans while samples with higher densities could also be traced using the tapping mode. The results of these AFM scans are shown in Fig. 1 over a long spectrum of aerosil densities. The surface roughness values of the samples were studied with respect to random disorder strength $\rho_{\rm s}$, which is given by Eq. (3) and was used in previous x-ray and heat-capacity measurements.
cpl-36-1-010501-fig1.png
Fig. 1. AFM scans of sample surfaces ranging from $\rho_{\rm s}=0.051$ g/cm$^3$ (a) to $\rho_{\rm s}=0.647$ g/cm$^3$ (g). These scans are collected with 256$\times$256 pixel resolution on a sample of 5$\times$5 µm$^2$ area for (a)–(e) and 2$\times$2 µm$^2$ area for (f) and (g). Between (a) and (e), there is a clear change in both the smoothness and the fractal structure of the surface. This change becomes dramatic for the samples shown in (f) and (g), as discussed in the text.
cpl-36-1-010501-fig2.png
Fig. 2. Profilometer microscope picture (A Ziess Axio CSM 700 type profilometer was used). (a) The actual surface image of the highest disordered strength sample $\rho_{\rm s}=0.647$ g/cm$^3$, while (b) is for the next one $\rho_{\rm s}=0.49$ g/cm$^3$.
As seen from $\rho_{\rm s}=0.051$ g/cm$^3$ (Fig. 1(a)), the surface is mostly composed of LC where a smooth surface topography, created by the gel-like structure of the sample, is observed. The small white colored sharp fractal-like regions were created by aerosil dispersion in the LC. These regions are more salient as $\rho_{\rm s}$ increases in the following panels. The dispersion of aerosil was thought to create a fractal network in the LC medium. This was previously discussed extensively in Refs. [3,4,15]. These sharp white small areas were the realization of 7 nm diameter aerosil spheres which come together to form diffused-aggregated regions starting at $\sim$30 nm in size for the first samples, as shown in Figs. 1(a) and 1(b). This corresponds to $\sim$4 and 5 silica particles. The hydrogen coated aerosil used in this experiment would form this kind of chemically fused fractal networks, which are weakly attached to each other.[15] Therefore, void length scales are formed for the LC molecules which in turn disorder their nematic features creating a random disorder effect on the nematic director. The random pinning effect of nematic director and short range disordered smectic phases were studied extensively for this material by x-ray diffraction techniques.[5,6,9-12,15] According to these experiments, the percolation limit was observed somewhat smaller than $\rho_{\rm s}=0.025$ g/cm$^3$. This is the reason why many previous experiments on these gel samples were started with a density of $\rho_{\rm s}=0.025$ g/cm$^3$. In fact, the most interesting physics lie in the vicinity of this density. However, the soft and sticky surface of LC+aerosil samples with $\rho_{\rm s}\sim0.025$ g/cm$^3$ did not allow unambiguous AFM scans. Thus in these experiments we could start our investigations only with $\rho_{\rm s}=0.051$ g/cm$^3$ density. It should also be emphasized that it was very difficult to obtain the results shown in Figs. 1(a) and 1(b). The main feature in Figs. 1(a)–1(c) is the dominant smooth LC surface with very low roughness values ranging from $\sim$8 to $\sim$13 nm, respectively. These values are listed in Table 1. In Fig. 1(d), the sample surface of $\rho_{\rm s}=0.22$ g/cm$^3$ is shown. As the aerosil mass density increases, the surface profile is found to be rougher than the ones in previous panels. This can be seen from the white regions which become more pronounced compared to less notable white regions of previous panels. The average size of these regions were measured to be $\sim$90 nm, creating a roughness of $\sim$33 nm. The increase in size of diffused aerosil aggregated regions can be seen from Figs. 1(e)–1(g), where the aerosil mass density increases to $\rho_{\rm s}=0.347$, 0.49 and 0.647 g/cm$^3$, respectively. These samples, which are more different than the ones shown previously, are found to be less gel-like, more solid and similar to small pebbles. The largest change is that the surface porosity has became much rougher. Especially for the highest $\rho_{\rm s}$ sample, the aggregation of aerosil forms aerosil groups, which are shown by white elongated spheres, $\sim$250 nm in size, meaning $\sim$35 silica particles. The aggregated silica groups bound to each other and formed even larger groups creating small hills, valley-like regions with crevices. These features covering the surface of the samples can reach a size of $\sim$3 in orders of magnitude larger than the features shown in Fig. 1. This is shown in Fig. 2(a) for $\rho_{\rm s}=0.647$ g/cm$^3$. Thus Fig. 2 shows the actual surface of the gel samples with entirely different scales compared to the ones shown in the previous figure. These aerosil groups and their surface appearances were also studied in aerosil tablet forms.[16,17] When we compare these results, the visual similarities are spectacular and this shows that starting with the $\rho_{\rm s}=0.347$ g/cm$^3$ sample, the volume and therefore the surface are dominantly composed of aerosils. The aerosil samples prepared in the tablet forms were composed and packed under certain pressure. In our understanding the applied pressure decreases the aerosil group size (GS: average size of the white colored droplet-like features on the very top of the surface) so that the measured GS values were a few tens of nm shorter but comparable to the values of our study. More importantly, the measured surface roughness values of polyethylene terephthatate PET based samples containing only 5% wt aerosil (even though the type of aerosil is different) are also comparable to the values listed in Table 1.[16,17] Overall, the aerosil aggregation and the surface topography are similar to our findings. This also confirms the very short random correlation lengths observed for the high aerosil mass density samples from x-ray scattering experiments.[9] Especially starting with $\rho_{\rm s}=0.347$ g/cm$^3$, $\xi_{\rm RD}$ becomes very short and saturates at $\sim$400, $\sim$500 Å for four different LCs; 8CB, 8OCB, 10CB and 408.[5,6,8,9-11] The saturated values calculated for $\xi_{\rm RD}$ do not vary much over these different LC molecules. This is basically another confirmation using only the surface profile information that the random perturbation observed in aerosil dispersed LCs are developed through the values of $\rho_{\rm s}=0.347$ g/cm$^3$ and that the latter is completed at these short length limits. In other words, if we continue to mix more aerosil in the same volume of the LC host, then the resultant gel will not introduce any other information than these two, three high density samples. The same conclusion would also be derived from the aerosil group size values listed in Table 1. The typical aerosil group size becomes almost saturated at $\sim$200–300 nm starting with $\rho_{\rm s}=0.347$ g/cm$^3$. As stated above, Fig. 2 shows the real picture from the surface of the $\rho_{\rm s}=0.647$ g/cm$^3$ sample. The large white colored droplet-like areas are the aerosil aggregated regions where the real surface roughness could reach up to almost $\sim$10 µm. This kind of high roughness could obviously only be measured by a profilometer. When we compare this surface with the ones of the $\rho_{\rm s}=0.49$ g/cm$^3$ sample, as shown in Fig. 2(b), we can see that we do not have any formations of these large white colored clusters. The surface of the $\rho_{\rm s}=0.49$ g/cm$^3$ sample is much smoother than the $\rho_{\rm s}=0.647$ g/cm$^3$ sample. The profilometer and the AFM measurements also show this numerically. Less disordered samples having more flat surfaces without any feature that can be seen by naked eyes are more difficult to measure with profilometers. The measurements become more unreliable mostly because of optic limitations.
Table 1. The length scales used in this study given as a function of random disorder strength. The units for $\rho_{\rm s}$ and $\rho$ are g/cm$^3$ while roughness $\langle R\rangle$, random correlation length $\xi_{\rm RD}$ and average aerosil group size GS are given in nm, Å and nm, respectively. The $\xi_{\rm RD}$ values were obtained from the previous 8CB+Aerosil and 8OCB+Aerosil x-ray diffraction experiments.[5,6,9,15] The $\xi_{\rm RD}$ results given in the last column belong to the 8CB+Aerosil data except the last two which correspond to the $\rho_{\rm s}$=0.49 g/cm$^3$ and $\rho_{\rm s}$=0.647 g/cm$^3$ samples. These are from the 80CB+Aerosil and 10CB+Aerosil experiments, respectively.[9,10,18] The average aerosil group size is measured on the pictures manually using the AFM analysis software.[13] The roughness values given for these two samples contain both AFM and profilometer results. The weight percentage of aerosil respect to total sample weight is given in the third column.
$\rho$ $\rho_{\rm s}$ wt% $\langle R\rangle$ $\xi_{\rm RD}$ GS
0.05 0.051 4.9 8.1$\pm$0.8 5516$\pm$105 $\sim$30
0.075 0.078 7.3 10.1$\pm$0.8 3844$\pm$70 $\sim$30
0.1 0.104 9.5 13.7$\pm$0.7 3250$\pm$70 $\sim$50
0.2 0.22 18 33.7$\pm$1.7 965$\pm$30 $\sim$90
0.3 0.347 26 45.5$\pm$2.3 415$\pm$12 $\sim$140
0.4 0.49 33 2000$\pm$$\sim$500 410$\pm$5 $\sim$210
160$\pm$8
0.5 0.647 39.5 10000$\pm$$\sim$2500 543$\pm$24 $\sim$250
180$\pm$$\sim$10
The overall roughness analysis of the whole sample spectrum is shown in Fig. 3. In this figure, the corresponding roughness values are given along with the random correlation lengths obtained from previous x-ray scattering experiments.[9] In doing so, we aim to show the correlation between the roughness and the short ranged ordering in the sample gels on the same graph. It has been observed that for high aerosil mass density samples, especially starting with $\rho_{\rm s}\sim0.347$ g/cm$^3$, different experiments with different LC samples having second-order phase transition yield the same or roughly the same lengths. The two Lorentzian (LZ+LZ$^2$) based line-shape analyses show a saturated-like $\xi_{\rm RD}$ region with $\sim$400 to $\sim$600 Å.[5,6,9-11,18] This is also one of the main reason why many heat capacity and x-ray studies focused on the low aerosil density spectrum $\rho_{\rm s} < 0.104$ g/cm$^3$ where the saturated values of $\xi_{\rm RD}$ were changing significantly with a small change in the aerosil mass density. Moreover, 8CB and 80CB have very close MacMillan ratios which confirm that the phase transitions seen in those LCs behave principally very close to each other.[19] Meanwhile, for 10CB, the structural behavior is entirely different, which shows first-order phase transition from its isotropic to smectic $A$ phase. However, the analyses performed on the 10CB+aerosil gels also show similar saturated $\xi_{\rm RD}$ values seen in 8CB and/or 8OCB samples especially for the high $\rho_{\rm s}$ region.[9] Therefore, we do not find any wrongdoing by including 8OCB+aerosil and 10CB+aerosil high disordered $\xi_{\rm RD}$ results in the comparison figures of Fig. 3 and Fig. 4. In addition, in these two figures almost all of the disordered LC density values are covered. The only missing density is $\rho_{\rm s}=0.025$ g/cm$^3$ when we compare with the previous experiments. Thus including the highly disordered sample data, as explained above, with the low aerosil density region covering almost all possible spectra of LC+aerosil gel, we believe that we strengthen the comparison and the following conclusions. In Fig. 3, as the aerosil mass density increases, so does the roughness $\langle R\rangle$ values while the random correlation length $\xi_{\rm RD}$ decreases. Both behaviors of $\langle R\rangle$ and $\xi_{\rm RD}$ are related to $\rho_{\rm s}$, exponentially. This is shown with the linear plots in Fig. 3. In Fig. 3(a) the comparison between $\langle R\rangle$ and $\xi_{\rm RD}$ include the profilometer roughness values for the two highest disordered samples. In Fig. 3(b) the same comparison is carried out solely using AFM roughness data. In the last panel, in contrast to from the previous panel, the image reflection of $\xi_{\rm RD}$ values depicted to bring out the similarities of the two different measurements. As the data is scaled as shown in Fig. 3(c), we can see only one form of exponential trend with respect to $\rho_{\rm s}$. This is depicted with a red colored line which helps guide the eyes. To show the same behavior in a logarithmic figure, we use the inverse $\xi_{\rm RD}$ multiplied with a constant amplitude of 10000. Hence, it is possible to show the correlation between $\langle R\rangle$ and $(\xi_{\rm RD})^{-1}$ clearly in logarithmic plot, given in Fig. 4. We believe that this figure is in fact the most important outcome of this study in which the two regional behaviors of low and high aerosil density data are enhanced using logarithmic $\langle R\rangle$ and $(\xi_{\rm RD})^{-1}$ values. The increase in aerosil mass density (the random field effect), which increases the random pinning of LC nematic orientation (so does the smectic layers), changes the correlation length of smectic-$A$ x-ray diffraction peaks while the same physical information can also be obtained from the surface topography of the LC+aerosil gels. In other words, as $\rho_{\rm s}$ increases, the sample becomes less correlated and rougher on the surface. Usually logarithmic figures tend to discern hidden or not-easily-seen features of such behavior like the one shown in Fig. 4. The increase in $\rho_{\rm s}$ creates an exponential increase in $\langle R\rangle$ and inverse $\xi_{\rm RD}$ which can be shown with a linear trend up to a certain value of $\rho_{\rm s}\sim0.38$ g/cm$^3$. After this disordered level, those two parameters vary monotonically, tracing like a saturation level. These two trends shown by red and blue colored lines (which are not a particular fit of any model, and simply give a guidance to the eye) are found to be in agreement.
cpl-36-1-010501-fig3.png
Fig. 3. Surface roughness and random correlation length versus random disorder strength. Surface roughness $\langle R\rangle$ and the correlation length $\xi_{\rm RD}$ listed in Table 1 are shown with respect to random disorder strength $\rho_{\rm s}$. (a) Roughness values include the profilometer data while in (b) only AFM results were shown with red colored data. (c) Image reflection of the $\xi_{\rm RD}$ values were used against the $\langle R\rangle$ values to clarify the correlation between these two parameters. The salient agreement between $\langle R\rangle$ and $\xi_{\rm RD}$ is shown with one line. All of the lines drawn on the data are only intended to guide the eyes, and they are not any kind of model fit.
For the completeness of the experiment, we also show $\langle R\rangle$ obtained by profilometer measurements, depicted by the solid squares (Fig. 4(a)). It should be noted that since these two values were measured by a completely different probe and both scale and the scan size were entirely different, we do not include them in our conclusions. We simply focus on the values obtained by AFM technique only when we draw our conclusion about the correlation between x-ray and AFM measurements. In Fig. 4(b), the similarities, and therefore the correlation between $\langle R\rangle$ and inverse $\xi_{\rm RD}$, are shown in a logarithmic scale for the important region of $\rho_{\rm s}=0.051$ g/cm$^3$ up to $\rho_{\rm s}=0.347$ g/cm$^3$. This region of the aerosil dispersion was studied extensively by many previous x-ray and heat-capacity experiments.[3,5,6,9-11,15,18,19] In Fig. 4(b), $(\xi_{\rm RD})^{-1}$ values are shown with six different aerosil density samples including the extra value for $\rho_{\rm s}=0.025$ g/cm$^3$.[5] As is clearly seen, the exponential behaviors of $\langle R\rangle$ and inverse $\xi_{\rm RD}$ with respect to $\rho_{\rm s}$ are very similar. Therefore, this provides evidence for the close correlation between these two parameters.
cpl-36-1-010501-fig4.png
Fig. 4. Inverse random correlation length $\xi_{\rm RD}^{-1}$ versus surface roughness $\langle R\rangle$ in a logarithmic plot. The collective correlation between $\xi_{\rm RD}$ (blue data and line) and $\langle R\rangle$ (red data and line) is depicted using the values calculated for $\xi_{\rm RD}^{-1}$. These values are also multiplied by a constant of 10000 to view the overall change with respect to the strength of disorder clearly in the picture. In (a), as $\rho_{\rm s}$ increases both $\langle R\rangle$ and $\xi_{\rm RD}^{-1}$ increase and then saturate for high $\rho_{\rm s}$. In (b), the same correlation is depicted for the more important region of aerosil densities of $\rho_{\rm s}\leq 0.347$ g/cm$^3$. The extra data point for $\rho_{\rm s}=0.0025$ g/cm$^3$ obtained from x-ray experiments was also added.[5] All of the lines drawn in this figure are for guiding purposes only and they are not intended to illustrate any kind of fit.
The very similar behavior seen between $\langle R\rangle$ and $\xi_{\rm RD}$ in Fig. 4(b) states that instead of performing an x-ray and/or a heat-capacity study we can reach the significant conclusions by measuring the roughness of the samples using AFM technique. This technique is much more simple and straightforward compared to the previous ones. Nevertheless, we introduce a new probe to investigate the interesting physics of random disordered LC+aerosil gels which was previously studied by long and complicated techniques of x-ray and heat-capacity. We also show the fractal base of aerosil dispersion in an LC host with real surface data for the first time. The change seen for $\langle R\rangle$ and $\xi_{\rm RD}$ shown in Fig. 4(a) resembles the evolution of the change from soft-gel to stiff-gel within the region of $\rho_{\rm s}\sim 0.1$ g/cm$^3$. This is first cited in Ref. [3] from the heat capacity results. The aerosil dispersion created a weak disorder, which is always much more interesting to work on, in the nematic to smectic $A$ phase transition and deep in the smectic $A$ phase. The gradual decrease in the long-range order of smectic $A$ was observed with the increase in the x-ray scattering widths.[5,6,8,9,12,13] Likewise, we encounter a change in the behavior of the $\langle R\rangle$ values of the surface topography in the vicinity of $\rho_{\rm s}\sim0.38$ g/cm$^3$ obtained by AFM on the 8CB+aerosil gels. The change in the trend of $\langle R\rangle$ respect to the increase in $\rho_{\rm s}$ can also be seen in the observed change of $\xi_{\rm RD}$. In this study, both low and high disordered regions of aerosil dispersion are studied. The effects on roughness values seen in the higher disordered region resembles more properly the disorder effects created by aerogel dispersion. This result is in agreement with the results of the previous experiments.[6,15] The soft and sticky surface for low concentrations of aerosil dispersed gels created difficult measurement conditions in order for a good AFM result to be obtained. A non-contact AFM scan for the lowest disordered density $\rho_{\rm s}=0.025$ g/cm$^3$ is found to be very difficult to perform, or is even impossible. We believe that further AFM studies will follow this first study, which will also focus on the topographical variations during the nematic to smectic $A$ phase transitions. In conclusion, we have investigated the LC+aerosil sample gels using their surface topography. The aerosil dispersion in the LC host creates fractal-like regions after a diffusion-limited aggregation process. This is seen from the surface topography from the low-to-high aerosil mass density samples. Depending on the aerosil amount in the LC host, we show that there is a net increase in the roughness value which can be used to characterize the sample surfaces. This result is correlated with the results of previous x-ray scattering experiments. The main overall outcome of this first study is being able to show that the random field effects on aerosil dispersed LC gels can be tracked using surface roughness. We believe that this is the first surface study of LC+aerosil gels. We also confirm the existence of quenched randomness. MR would like to thank Professor Birgeneau for his support and constructive comments. MR also acknowledge Professor Garland who introduced the great wonder world of LCs. Professor Garland and his great work with LCs will be remembered for as long as we keep working in this area. References Calorimetric study of phase transitions for octylphenylthiolpentyloxybenzoate in silica aerogelsEffect of silica aerosil particles on liquid-crystal phase transitionsCalorimetric and small angle x-ray scattering study of phase transitions in octylcyanobiphenyl-aerosil dispersionsNematics with Quenched Disorder: What Is Left when Long Range Order Is Disrupted?Hydrogen-bonded silica gels dispersed in a smectic liquid crystal: A random field XY systemSmectic ordering in liquid-crystal–aerosil dispersions. I. X-ray scatteringHigh-resolution x-ray scattering study of the effect of quenched random disorder on the nematic–smectic- A transitionFirst-order isotropic–smectic- A transition in liquid-crystal–aerosil gelsHigh-resolution x-ray study of nematic–smectic- A and smectic- A –reentrant-nematic transitions in liquid-crystal–aerosil gelsSmectic- A and smectic- C phases and phase transitions in 8 ¯ S 5 liquid-crystal-aerosil gelsSmectic ordering in liquid-crystal–aerosil dispersions. II. Scaling analysisSurface characterization of polyethylene terephthalate/silica nanocompositesSintering process of amorphous SiO2 nanoparticles investigated by AFM, IR and Raman techniquesEffect of a quenched random field on a continuous symmetry breaking transition: Nematic to smectic- A transition in octyloxycyanobiphenyl-aerosil dispersionsCritical behavior at nematic–smectic- A phase transitions
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