I noticed the hard sign 'ъ' (твёрдый знак) is not present and used in the Ukrainian language in comparison with Russian; why is this?
Why should it?
I know two modern use-cases for hard sign:
In Russian it can be used between a consonant and an iotified vowel to specify that the following iotified vowel should sound as in the beginning of the word, not as it usually sounds when placed after a consonant. In Ukrainian we just put apostrophe for that. (In Russian they sometimes used apostrophe too, but hard sign is more standard in Russian.)
In Bulgarian it can be used to specify mid back unrounded vowel (IPA /ɤ̞/). We don't have such sound in Ukrainian.
Update. I noticed that you're asking explicitly about Russian. Sorry, I didn't notice it initially. Probably in that case we need to dive in the history a bit.
The Old East Slavic language, which was used on the territory of the Kievan Rus' (predecessor of modern Belarus, Ukraine and Russia) at least as a written language (some claim that it was also used as an oral language while other think that the oral language of that time was quite different), did use both ъ (hard sign) and ь (soft sign). However their meaning was originally quite different than in modern Russian and Ukrainian languages — both ъ and ь meant extra-short vowels. In fact, at that times, Old East Slavic allowed only open syllables (every syllable had to end with a vowel, and ъ/ь were both vowels).
Since approximately the XI century, extra-short vowels start to disappear from the Old East Slavic language and the language started to allow closed syllables. In some cases ъ and ь were replaced by о, е and other vowels, in some cases they just dropped out. They didn't immediately disappear from writing, writers often continued to traditionally put ъ and ь in old places for a long time after they were replaced or disappeared in pronunciation.
But the larger distance emerged between the written language and the oral language the harder it was for writers to put ъ and ь consistently (such “mistakes” are actually the thing that helps modern researchers to explore evolution of the oral dialects — as there was no audio-recording hardware in medieval/pre-medieval times).
At the turn of the XIX and XX centuries, the Russian language:
- used ь (soft sign) only for softening the preceding consonant (I don't know exactly how such role actually appeared; probably it's a rudiment of the original ь's role, i.e. when ь sounded like a vowel it also sometimes palatalized preceding consonant); additionally it made the following iotified vowel to sound it usually sounds in the beginning of the word or after a vowel (which is natural for ь as it was originally a vowel);
- used ъ (hard sign) mostly as an aimless traditional character; additionally it made the following iotified vowel to sound like in the beginning of the word or after a vowel (which is natural for ъ; but was probably only a minority of ъ usages). In the beginning of XX a reform of the Russian language eliminated that aimless-traditional use ъ from Russian (as for now, it's used only to make the following iotified vowel to sound like in the beginning of the word or after a vowel).
The Ukrainian language used almost the same writing system (with some differences in traditions) as Russian at least till the end of the XVIII century. XIX was relatively experiment-rich century for the Ukrainian language: at least 10 different writing systems were proposed by different Ukrainian authors in XIX, some of which were quite radical. Many of them abandoned “dead” Cyrillic letters long before they were eliminated by the corresponding reform in Russian. Under such circumstances there seems to be no strong reasons to keep using ъ.
In fact, apostrophe fits its role (which is handled by ъ in modern Russian) quite well. The fact is that both Ukrainian and Russian have so-called iotified vowels (which sound in certain style when they're placed right after a consonant and in the other style in other cases, i.e. in the beginning of the word or right after vowel). And apostrophe or dash are quite intuitive symbols to “break” a word and to make the following letter to sound like in the beginning of the word. Unofficially apostrophe was sometimes used in the same role (i.e. instead of ъ) in the Russian language too (especially in 1920-1930th), though it was never officially adopted for that role there.
I would like to notice another thinghs to Sasha.
- Belarusian also uses apostrophe as Ukrainian instead ъ;
- Same for North Macedonian but for Bulgarian ъ and, as I can see, it’s rare things;
- Cyrillic ex-Yugoslavia languages just removed iotation vowels and created soft consonants like ђ, ћ, њ, љ… — for last 2 you can see ь.
Ukrainian already had (and still can) variation like Serbian which known as drahomaniwka: here is no apostrophe or ъ, no iotations vowels (Ukrainian already uses this for йо/и, ьо/и) and soft consonants which Ukrainian has so much.